On surface completion and image inpainting by biharmonic functions: Numerical aspects

TL;DR

This paper explores numerical methods for surface completion and image inpainting using biharmonic functions, focusing on finite difference schemes and boundary data involving Laplacian and normal derivatives.

Contribution

It introduces detailed finite difference schemes for biharmonic functions based on boundary data, advancing numerical techniques for surface and image inpainting.

Findings

Effective finite difference schemes for biharmonic functions are developed.

Numerical experiments demonstrate the viability of the methods for surface and image inpainting.

Boundary data involving Laplacian and normal derivatives improve inpainting results.

Abstract

Numerical experiments with smooth surface extension and image inpainting using harmonic and biharmonic functions are carried out. The boundary data used for constructing biharmonic functions are the values of the Laplacian and normal derivatives of the functions on the boundary. Finite difference schemes for solving these harmonic functions are discussed in detail.